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slope angle

The slope angleαα\alpha of any line in ℝ2superscriptℝ2\mathbb{R}^{2} is the angle between the line and xxx-axis; in the case that the line is descending, the angle is negative. We always have that -90∘<α≤90∘superscript90αsuperscript90-90^{{\circ}}<\alpha\leq 90^{{\circ}}.

In some mathematical works, the slope angle of a line in ℝ2superscriptℝ2\mathbb{R}^{2} is defined to be the angle measured from the positivexxx-axis to the line in the counterclockwise direction. This definition has some drawbacks because slope angles are then allowed to be obtuse but can no longer be negative. When this definition is used, the formulaα=arctan⁡mαm\alpha=\arctan{m} no longer holds. The convention in PlanetMath is to use the former definition.